Negotiations over how to extend a payroll tax holiday for 160 million Americans and avoid a government shutdown this weekend ground to a halt Wednesday after a standoff in the Senate over how to proceed.

Amid the gridlock, Cabinet secretaries for the first time formally alerted affected federal workers Wednesday to the possibility of a shutdown — indicating in an ­e-mail that they would determine later which staffers are “essential” to maintain operations in the event of a funding disruption.

If there was any sign of progress, it was that Senate Democratic leaders met with President Obama on Wednesday at the White House to weigh whether to drop their demand that the $120 billion payroll tax cut be paid for with a new surtax on millionaires. Republicans have rejected the idea, but it was not clear Wednesday whether that concession from Democrats would be enough to produce a deal.

With a Friday deadline fast approaching, the threat of a shutdown grew more urgent as a separate omnibus spending bill remained stalled. House Republicans are pursuing a go-it-alone approach on the spending bill, essentially daring Democrats to vote against a deal — bringing closer the prospect of a shutdown at the end of the week, when a short-term funding measure expires.

Senate Majority Leader Harry M. Reid (D-Nev.) said he wanted the vote to prove that the House measure lacks support — a first step, he said, to forcing negotiations on a compromise.Under Senate rules, Democrats can demand a vote on the bill on Saturday but would need members’ unanimous consent to vote before then.

“The sooner we put this useless partisan charade behind us, the sooner we can negotiate a solution that protects middle-class workers,” Reid said.

But Senate Minority Leader Mitch McConnell (R-Ky.) insisted that the Senate should first take up the spending measure, which would keep the government funded through September.

Republicans say bipartisan negotiators have reached a deal on the spending bill. But they say the White House and Reid will not allow a final vote on the measure, holding the bill hostage and threatening a shutdown to increase Democratic leverage on the payroll tax issue.

Once the spending bill passes, House members can go on their holiday break, leaving Senate Democrats with the unpleasant choice of accepting the House’s payroll tax bill, or rejecting it and taking the blame for allowing the tax break to expire.

House Republicans huddled for two hours late Wednesday to discuss whether to proceed with a vote on the spending bill, even without a Democratic sign-off.

That could prove tricky. Many conservatives object to the bill’s $1.043 trillion spending level, negotiated by Democrats and Republicans in the August debt deal, and it’s not clear whether the bill could pass without some Democratic support.

A White House spokesman said late Wednesday that Obama has a number of concerns with the spending bill and called on Congress to adopt a stopgap measure to keep the government open a few days more while talks continue.

House Speaker John A. Boehner (R-Ohio) told reporters late Wednesday that no decisions had been made, but that the House had acted to extend the tax cut and now it was the Senate’s turn.

“I’m tired of hearing what the Senate can’t do,” he said. “I think it’s time for us to wait and see what the Senate can do.”

The day’s events highlighted the fact that neither side has come up with a way to pay for the tax cut that can get the 60 votes necessary for Senate approval.

Senate Democrats say that the House bill is unacceptable and that they will vote against it, and the White House has said President Obama would veto it.

Their objections center on several GOP initiatives added to the bill to attract votes from conservatives, many of whom would not support the tax cut extension otherwise. They include a reduction in unemployment benefits, new rules that could require the unemployed to take drug tests and enroll in GED programs to receive benefits, and the delay of new regulations on boiler emissions.

They also include an extension of a pay freeze for federal workers and higher Medicare premiums for upper-income seniors. And the two sides are clashing over a provision that would force a decision on a construction permit for the Keystone XL pipeline within 60 days. The State Department, which is reviewing the pipeline issue, has said that if forced to make a decision so quickly, it would have to deny the permit.

If the dispute resulted in a shutdown, not all agencies and departments would be affected, thanks to a partial spending bill passed in November. The departments of Agriculture, Commerce, Housing and Urban Development, Justice, State, and Transportation, as well as NASA and some other smaller agencies, would be spared.

But much of the government would be shuttered — national parks would close, for instance, and processing of some passports would cease. The showdown marks the fourth time this year that congressional disputes have dragged the government to the brink of a partial shutdown.

Behind the white-hot rhetoric of their leaders, many rank-and-file lawmakers continued to predict that a last-minute compromise would extend the tax cut and prevent a shutdown. A number wearily said that the only casualty of the fight would be Congress’s already battered reputation.

“It’s all going to get passed eventually,” said Sen. Tom Coburn (R-Okla.). “But the political maneuvering is sickening.”